What does the circled portion represent in the confidence interval formula?
p±z.
O Sample proportion
O Margin of error
p(1-p)
n
Confidence interval
O Sample Size

Answer:

First, substitute x for 2 in 7x+5=21.

7 * 2 = 14 + 5 = 19

x = 2 is not a solution of 7x+5=21.

For this exercise you need to use the following formula:

Where "FV" is the future value, "PV" is the present value, "r" is the interest rate (in decimal form), and "n" number of periods.

In this case, analyzing the information given in the exercise, you can identify that:

Remember that a percent can be written in Decimal form by dividing it by 100. Then:

Since she earns interest at 3% per annum and it is compounded monthly, you can determine that the interest rate per month is:

Knowing that 1 year has 12 months, you know that:

Then:

Therefore, you can substitute all those values into the formula and then evaluate, in order to find the future value of Joan’s investment after 1.5 years:

Hence, the answer is: $209.19 (approximately).

Answer:

B. 5

Step-by-step explanation:

In order to estimate how many pizzas were eaten, we need to subtract the amount of pizza left from the original amount. The amount of pizza left is 5/6 + 1 3/4. 5/6 is about 1 and 1 3/4 is about 2. 1 + 2 = 3 pizzas eaten.

The original amount of pizzas, 8, minus the amount of pizzas eaten, 3, is 5.. We can estimate that 5 pizzas were eaten.

Answer:

x = (v - u) / a

Step-by-step explanation:

v = u + ax.

subtract u from both sides:

v - u = ax.

divide both sides by a:

(v - u) / a = x.

so x = (v - u) / a.

this can also be written v/a - u/a

As a result of the above transactions and using the national income formula, the national income A. rises by $175,000.

The formula for calculating the national income here is Rent + Wages + Interest + Profit + Mixed-Income.

Lost annual wages = $30,000

Profit from sale of firm = $200,000

Consultant fee (mixed income) = $8,000

Occupational pension (mixed income) = $9,000

Assistant's wages lost = $12,000

$0+ -$30,000 -$12,000 + $0 + $200,000 + $8,000 + $9,000

= -$42,000 + $217,000

National income = $175,000

Thus, as a result of the above transactions and using the national income formula, the national income A. rises by $175,000.

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The set of whole numbers, the set of integers, and the set of rational numbers are closed under each of the four basic operations.

Whole numbers:

Addition: Yes

Subtraction: No (e.g. 5 - 7 = -2)

Multiplication: Yes

Division: No (e.g. 4 ÷ 2/3 is not a whole number)

Integers:

Addition: Yes

Subtraction: Yes

Multiplication: Yes

Division: No (e.g. 4 ÷ 1/2 is not an integer)

Rational numbers:

Addition: Yes

Subtraction: Yes

Multiplication: Yes

Division: Yes (provided the denominator is non-zero)

Polynomials:

Addition: Yes

Subtraction: Yes

Multiplication: Yes

Division: No (in general, polynomials cannot be divided by other polynomials)

Polynomials are like rational numbers with respect to closure under addition, subtraction, and multiplication.

However, they are not closed under division like rational numbers.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.

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The value of x in the expression fraction 20 Over x is 10.

An expression in maths is a sentence with a minimum of two numbers or variables and at least one maths operation. The expression can be explained as a statement which consist of numbers, variables, and some arithmetical operations.

an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Numbers, symbols and operators (such as + and ×) grouped together that show the value of something. Examples: • 2 + 3 is an expression. • 3 − x/2 is also an expression.

Given that, 20 Over x = 2

Converting into mathematical expression, we get,

20÷x = 2

20/x = 2

Cross multiplying,

20/2 = x

x = 10

Hence, the expression fraction 20 Over x satisfies at x = 10

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The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

Number = 14

Step-by-step explanation:

It is given that,

Twice the sum of a number and seven is three times the number

Let the number be x. Twice of the number is 2x. Three times of the number is 3x.

So,

2(x+7)=3x is the equation that models the given scenario

Opening brackets on LHS,

2x+14=3x

Subtracting 2x on both the sides

2x-2x+14=3x-2x

14=x

So, the number is 14.

The number is 14.

The calculation is as follows:

Based on the above information, the calculation is as follows:

2(x+7)=3x  

2x+14=3x

x = 14

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The equation for every number whose cube is equal to -2 is ∀x∈R|x³=2.

Mathematical logic is one of the languages that deal with logical arguments and their operations with each other to infer and come up with decisions.

It has its own syntax and a logical expression is a statement that represents a logical argument in the form of mathematical logic terms. there are two types of quantifiers:

1) Universal quantifier: (for all, ?)

2) Existential quantifier: (there exists, ?)

The following are also the logical operations:

1) ?: conjunction

2) V: disjunction

3) ?: Conditional

4) ?: Biconditional

5): not

The equation for every number whose cube is equal to 2 is ∀x∈R|x³=2

The equation for the square of every number is at least 0 is ∀x∈R x²≥0.

The equation for the number that is equal to its square is ∀x∈R x²=0.

The equation for every number that is less than or equal to its square is ∀x∈R x≤x².

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The coordinates of the intersection of the diagonals of abcd with the given vertices are (0,2).

The equation of diagonal AC is the equation of the line joining

(−4,6) and (4,−2)

Using the two point formula of a line, we have

           (y−6) / (x+4) = 6−(−2) / (−4−4)

                       x + y = 2

The equation of diagonal BD is the equation of the line joining

(5,6) and (−5,−2)

Using the two point formula of a line, we have

           (y−6) / (x−5) = 6−(−2) /  5−(−5)

                           5y = 4x+10

Multiply equation x + y = 10 by 5 to get 5x+5y=10

Replace 5y=4x+46 using 5x+5y=10

        5x + (4x+10) = 10

        5x + 4x +1 0 = 10

           9x + 10 = 10

               9x=0

                 x=0

Substitute x=0 in eqn(1), To get 0+y=2

                                                         y=2

The point of intersection of the diagonals of the given quadrilateral is (0,2)

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Answer:

5(2y +1)

Step-by-step explanation:

simplest form =10y+5

-11.9 -1 = -12.9

Your answer is negative 12.9

Answer:

-12.9

Step-by-step explanation:

Hope this helps you! :)

Answer:

-5

Step-by-step explanation:

The y coordinate of the vertex is -5.

We can answer this by the rule of three.

Then:

Therefore his score will be 90 points.

Answer:

(f-g)(x) = 3x^3+8x^2-9x+2

Answer:

B

Step-by-step explanation:

Answer:

\(Width = 36in\)

\(Size = 42.02\)

Step-by-step explanation:

Given

\(x \to width\)

\(y \to height\)

\(x : y = 16 : 9\)

Required

The size of \(screen\) of height \(20,6in\)

First, we calculate the width using the following equivalent ratios

\(16: 9 = x : 20.6\)

Express as fraction

\(\frac{16}{ 9} = \frac{x }{ 20.6}\)

Solve for x

\(x = 20.6 * \frac{16}{ 9}\)

\(x = 36.62\)

Hence:

\(Width = 36in\) --- approximated

So, we have:

\(x = 36.62\)

\(y =20.6\)

The size (diagonal) is then calculated using:

\(Size = \sqrt{x^2 + y^2\)

\(Size = \sqrt{36.62^2 + 20.6^2\)

\(Size = \sqrt{1765.3844\)

\(Size = 42.02\)

\(Size =42in\) --- approximated

On solving the provided question, we got that 18 no. of glasses of punch was Lucas able to fill

a mathematical procedure. The most frequent operations are add, subtract, multiply, and divide . However, there are numerous others, including squaring, taking the square root, logarithms, etc. If it's not a number, it's probably an operation.

9/2= quarts of iced tea

9/4= quarts of lemonade

After mixing,

punch for a party = 9/2 + 9/4 = 27/4

He fills 3/8 =  quart of punch

No. of glasses of punch was Lucas able to fill = 27/4 X  8/3  = 18

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Answer:

1.62533254

Step-by-step explanation:

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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The number of people that nare expected to vote in the election is 260,000. people.

Simply put, a fraction is a portion of a whole. Mathematically, the number is represented as a quotient with split numerator and denominator. The numerator and denominator of a simple fraction are both integers. On the other hand, a complex fraction has a fraction in either the numerator or the denominator.

In this situation, the pre-election survey showed that two out of every three eligible voters would cast ballots in the county election and there are 390,000 eligible voters in the county.

The number of people expected to vote will be:

= Fraction of expected voters × Total number of people

= 2/3 × 390000

= 2 × 130000

= 260000

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Answer:

P(<18) = 0.17

Step-by-step explanation:

To find the probability, put the under 18s on top of a fraction and put the total population on the bottom of a fraction, like this:

251/1487

Then you can divide it. Use a calculator or long division with pencil and paper.

251/1487

= 0.168796

Round to two places.

~= 0.17

The temperature T of the coffee after 10 minutes is 100.

Two or more expressions with an Equal sign is called as Equation.

change of temperature of an object is proportional to the difference between its temperature and the temperature of its surroundings.

dT/dt = -k(T - t)

dT/dt is the rate of change of temperature,

T is the temperature of the coffee,

t is the temperature of the room, and k is a constant of proportionality

We need to find the temperature of coffee after 10 minutes

∫(dT/T - kdt) = -∫kdt

ln(T) - kt = -kt + C

we can use the initial condition that the temperature of the coffee is 100°C at t = 0:

ln(100) - 0 = -0 + C

C = ln(100)

ln(T) - kt = -kt + ln(100)

ln(T) = -kt + ln(100) + kt

ln(T) = ln(100)

T = 100e⁰

T = 100

Hence, the temperature T of the coffee after 10 minutes is 100.

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Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.

To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:

Assumptions:

Tax depreciation is straight-line over five years.

Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.

Tax on salvage value is 30% of the difference between salvage value and book value of the investment.

The cost of capital is 12%.

Given:

Initial investment cost = $50,000

Useful life of the equipment = 5 years

To calculate the depreciation expense each year, we divide the initial investment by the useful life:

Depreciation expense per year = Initial investment / Useful life

Depreciation expense per year = $50,000 / 5 = $10,000

Now, let's calculate the book value at the end of each year:

Year 1:

Book value = Initial investment - Depreciation expense per year

Book value \(= $50,000 - $10,000 = $40,000\)

Year 2:

Book value = Initial investment - (2 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (2 \times$10,000) = $30,000\)

Year 3:

Book value = Initial investment - (3 \(\times\) Depreciation expense per year)

Book value = $50,000 - (3 \(\times\) $10,000) = $20,000

Year 4:

Book value = Initial investment - (4 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (4 \times $10,000) = $10,000\)

Year 5:

Book value = Initial investment - (5 \(\times\) Depreciation expense per year)

Book value \(= $50,000 - (5 \times $10,000) = $0\)

Based on the assumptions, the salvage value is $10,000 in Year 5.

If the asset is scrapped in Year 4, the salvage value is $15,000.

To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:

Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)

For Year 5:

Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)

For Year 4 (if scrapped):

Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)

Now, let's calculate the after-tax cash flows for each year:

Year 1:

After-tax cash flow = Depreciation expense per year - Tax on salvage value

After-tax cash flow = $10,000 - $0 = $10,000

Year 2:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 3:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $0 - $0 = $0

Year 4 (if scrapped):

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $15,000 - $1,500 = $13,500

Year 5:

After-tax cash flow = Salvage value - Tax on salvage value

After-tax cash flow = $10,000 - $3,000 = $7,000

Now, let's calculate the net present value (NPV) using the cost of capital of 12%.

We will discount each year's after-tax cash flow to its present value using the formula:

\(PV = CF / (1 + r)^t\)

Where:

PV = Present value

CF = Cash flow

r = Discount rate (cost of capital)

t = Time period (year)

NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment

Let's calculate the NPV:

PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)

PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)

PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)

PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)

PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)

NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000

NPV = $22,954.24 - $50,000

NPV = -$27,045.76

The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.

Therefore, the investment may not be favorable.

Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.

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The complete question may be like :

Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.

You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.

Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.

Answer:

263.76in^2

Step-by-step explanation:

210/360*3.14*12*12

7*3.14*12

263.76

Answer:

6x

Step-by-step explanation:

Area of triangle = l x w => 2x x 3x = 6x